Expect to be able to max out EV on two chosen stats as well as bring another one about 1/4 way through on the
diagram scale. Haven't got any solid numbers on individual stat or total EV cap.
Super training (the ball games) will be your main source of EV points, easy and fun. It is available from the start of the game in the lower screen. There are three difficulty levels with six games each, one for each stat. These games also reward you with bags specific to the stat of the game. When you manage to win within the set time limit in every game on all levels you unlock secret training, where you get items as prizes.
Maxing a single stat through super training can take as little as about 25 minutes.
Base training will give you punching bags you use beforehand that either give you advantages in the super training, like doubling the prize points or increasing your movement speed. Other bags can directly award you with EV points. These particular bags come in 6 variations, one for each stat, in three different sizes: Small, Medium and Large. Small gives 1 point, Medium gives 4 points and Large gives 12 points. Overall, seeing as you only have room for 12 bags at a time, Large bags are superior. Punching the default bags gives you bags at random and does not automatically apply EV points or the like.
Finally, one of the bags is called a Reset bag, it resets the EV points you acquired through this type of training as well as the ones gained through the traditional method of battle. It's easiest to acquire by just punching the default "empty" bag until one drops. The secret levels may give one as a prize too but its random. As for level 100, i cannot say for sure how it will affect them but super training will be viable for them too so reseting their EV should be possible. Trades should carry over fine and their EV can most likely be reset.
New guys, remember to always EV train as soon as you get the pokemon. For now i don't know whether losses due to late EV training has been changed or how much of the basics the developers has altered.
UPDATE: Went through every secret super training level (there are 2 with six games each) and have every medal that you receive for succeeding within a certain time-frame. No extra boost in EV, but you get relatively rare items as prizes plus a punching bag. The fifth game in the second (and final) secret level gave me for example a pp-up.
UPDATE 2: Edited the original wall of text and added more info. Don't you tl;dr me!
EDIT:
Example of chart and maximum EV distribution for the curious [Small spoiler on the Pokemon]
